Diffusion from First Principles: From Data to Noise and Back
The one idea behind every diffusion model — gradually destroy structure with noise, then learn to undo it — with an interactive forward-diffusion explorable to build intuition.
Technical notes that explain ideas from first principles: how air traffic control works as a safety-critical control system, and how diffusion and flow-matching models are built. Several notes include interactive explorables that run in the browser.
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The one idea behind every diffusion model — gradually destroy structure with noise, then learn to undo it — with an interactive forward-diffusion explorable to build intuition.
The Gaussian is the workhorse of generative modeling. Here's everything you need — mean, covariance, and the one trick (x = μ + σε) that makes diffusion trainable.
How Air Traffic Control keeps order in a crowded sky: separation, sequencing, and flow management viewed as a predictive, safety-critical control system.